It's a bit simpler than this article outlines. How much you are remembered is based on what your accomplishments/stores/press/etc are recorded in.

For example, if you were a world renowned inventor and everyone wrote and communicated about you via clay pots then your memory is only carried on as a function of how many clay pot readers there are. Since all clay pot readers are dead and the medium itself is dead, your memory is dead. This is assuming no one transcribed the text from clay pots to whatever new communication medium came next.